\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t29\_glib\_004 (TMaMbNWWBgzBVBua5gHLH8FsKfvk7gr7Ffd)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_glib\_000 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_glib\_003 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_glib\_003 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k14\_glib\_004 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_glib\_004 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_subset\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{X0}}~{({{{k2\_xboole\_0}~{X0}}~{X1}})}}}}\label{hyp:ehhdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (k1\_xtuple\_0~(k4\_tarski~X0~X1)=X0){\unicdcdcdhd}(k2\_xtuple\_0~\\
(k4\_tarski~X0~X1)=X1)\end{array}
\label{hyp:ehhdpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_glib\_000~X0){\unicdcdcdhd}((v1\_glib\_003~X0){\unicdcdcdhd}\\
(v7\_glib\_003~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k2\_zfmisc\_1~\\
(k1\_zfmisc\_1~(k6\_glib\_000~X0))~(k1\_zfmisc\_1~(k7\_glib\_000~X0)))){\unicdbdjdcd}\\
(\preoh (k12\_glib\_004~X0~X1{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k6\_glib\_000~X0)){\unicdbdjdcd}(\preoh (\preoh X2 \in k2\_domain\_1~(k1\_zfmisc\_1~(k6\_glib\_000~\\
X0))~(k1\_zfmisc\_1~(k7\_glib\_000~X0))~X1){\unicdcdcdhd}(k14\_glib\_004~X0~X1=k4\_tarski~\\
(k4\_subset\_1~(k6\_glib\_000~X0)~(k2\_domain\_1~(k1\_zfmisc\_1~(k6\_glib\_000~\\
X0))~(k1\_zfmisc\_1~(k7\_glib\_000~X0))~X1)~(k6\_domain\_1~(k6\_glib\_000~\\
X0)~X2))~(k2\_xboole\_0~(k3\_domain\_1~(k1\_zfmisc\_1~(k6\_glib\_000~\\
X0))~(k1\_zfmisc\_1~(k7\_glib\_000~X0))~X1)~(k1\_tarski~(k10\_subset\_1~\\
(k12\_glib\_004~X0~X1)))))))))\end{array}
\label{hyp:ehcdidpfhgmgjgcgpfadaded}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{X0}}~{X0}}}}\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}(k3\_domain\_1~X0~X1~\\
X2=k2\_xtuple\_0~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}(k2\_domain\_1~X0~X1~\\
X2=k1\_xtuple\_0~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {\preoh{{{v1\_xboole\_0}~{({{k1\_zfmisc\_1}~{X0}})}}}}}\label{hyp:ggdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_glib\_000~X0){\unicdcdcdhd}((v1\_glib\_003~\\
X0){\unicdcdcdhd}(v7\_glib\_003~X0))))))){\unicdcdcdhd}(m1\_subset\_1~X1~(k2\_zfmisc\_1~(k1\_zfmisc\_1~\\
(k6\_glib\_000~X0))~(k1\_zfmisc\_1~(k7\_glib\_000~X0))))){\unicdbdjdcd}(m1\_subset\_1~\\
(k14\_glib\_004~X0~X1)~(k2\_zfmisc\_1~(k1\_zfmisc\_1~(k6\_glib\_000~X0))~\\
(k1\_zfmisc\_1~(k7\_glib\_000~X0))))\end{array}
\label{hyp:egehpflgbdedpfhgmgjgcgpfadaded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_glib\_000~X0){\unicdcdcdhd}((v1\_glib\_003~X0){\unicdcdcdhd}\\
(v7\_glib\_003~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k2\_zfmisc\_1~\\
(k1\_zfmisc\_1~(k6\_glib\_000~X0))~(k1\_zfmisc\_1~(k7\_glib\_000~X0)))){\unicdbdjdcd}\\
(((k12\_glib\_004~X0~X1=k1\_xboole\_0){\unicdbdjdcd}(k14\_glib\_004~X0~X1=X1)){\unicdcdcdhd}\\
(((k1\_funct\_1~(k10\_glib\_000~X0)~(k10\_subset\_1~(k12\_glib\_004~\\
X0~X1)) \in k2\_domain\_1~(k1\_zfmisc\_1~(k6\_glib\_000~X0))~(k1\_zfmisc\_1~\\
(k7\_glib\_000~X0))~X1){\unicdbdjdcd}((k12\_glib\_004~X0~X1=k1\_xboole\_0){\unicdcdcdid}(k14\_glib\_004~\\
X0~X1=k4\_tarski~(k2\_xboole\_0~(k2\_domain\_1~(k1\_zfmisc\_1~(k6\_glib\_000~\\
X0))~(k1\_zfmisc\_1~(k7\_glib\_000~X0))~X1)~(k1\_tarski~(k1\_funct\_1~\\
(k11\_glib\_000~X0)~(k10\_subset\_1~(k12\_glib\_004~X0~X1)))))~(k2\_xboole\_0~\\
(k3\_domain\_1~(k1\_zfmisc\_1~(k6\_glib\_000~X0))~(k1\_zfmisc\_1~(k7\_glib\_000~\\
X0))~X1)~(k1\_tarski~(k10\_subset\_1~(k12\_glib\_004~X0~X1))))))){\unicdcdcdhd}\\
(\preoh (k12\_glib\_004~X0~X1{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((\preoh (k12\_glib\_004~X0~X1{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}\\
(k1\_funct\_1~(k10\_glib\_000~X0)~(k10\_subset\_1~(k12\_glib\_004~X0~\\
X1)) \in k2\_domain\_1~(k1\_zfmisc\_1~(k6\_glib\_000~X0))~(k1\_zfmisc\_1~\\
(k7\_glib\_000~X0))~X1)){\unicdcdcdhd}(k14\_glib\_004~X0~X1{\unicdcdgdad}k4\_tarski~(k2\_xboole\_0~\\
(k2\_domain\_1~(k1\_zfmisc\_1~(k6\_glib\_000~X0))~(k1\_zfmisc\_1~(k7\_glib\_000~\\
X0))~X1)~(k1\_tarski~(k1\_funct\_1~(k10\_glib\_000~X0)~(k10\_subset\_1~\\
(k12\_glib\_004~X0~X1)))))~(k2\_xboole\_0~(k3\_domain\_1~(k1\_zfmisc\_1~\\
(k6\_glib\_000~X0))~(k1\_zfmisc\_1~(k7\_glib\_000~X0))~X1)~(k1\_tarski~\\
(k10\_subset\_1~(k12\_glib\_004~X0~X1))))))))))\end{array}
\label{hyp:egbdfdpfhgmgjgcgpfadaded}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpfhgmgjgcgpfadaded}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_glib\_000~X0){\unicdcdcdhd}((v1\_glib\_003~X0){\unicdcdcdhd}\\
(v7\_glib\_003~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k2\_zfmisc\_1~\\
(k1\_zfmisc\_1~(k6\_glib\_000~X0))~(k1\_zfmisc\_1~(k7\_glib\_000~X0)))){\unicdbdjdcd}\\
((r1\_tarski~(k2\_domain\_1~(k1\_zfmisc\_1~(k6\_glib\_000~X0))~(k1\_zfmisc\_1~\\
(k7\_glib\_000~X0))~X1)~(k2\_domain\_1~(k1\_zfmisc\_1~(k6\_glib\_000~\\
X0))~(k1\_zfmisc\_1~(k7\_glib\_000~X0))~(k14\_glib\_004~X0~X1))){\unicdcdcdhd}(r1\_tarski~\\
(k3\_domain\_1~(k1\_zfmisc\_1~(k6\_glib\_000~X0))~(k1\_zfmisc\_1~(k7\_glib\_000~\\
X0))~X1)~(k3\_domain\_1~(k1\_zfmisc\_1~(k6\_glib\_000~X0))~(k1\_zfmisc\_1~\\
(k7\_glib\_000~X0))~(k14\_glib\_004~X0~X1)))))\end{array}$$
\end{theorem}
\end{document}
